What is the solution to the system of equations? \( \left\{\begin{array}{l}5 x-4 y=-2 \\ 2 x+4 y=16\end{array}\right. \)

To solve the system of equations, we can use the substitution or elimination method. For simplicity, let's use the elimination method. First, we'll rearrange the equations: 1. \( 5x - 4y = -2 \) 2. \( 2x + 4y = 16 \) Next, we'll add these two equations together to eliminate \(y\): \[ (5x - 4y) + (2x + 4y) = -2 + 16 \] This simplifies to: \[ 7x = 14 \implies x = 2 \] Now, substitute \(x = 2\) back into one of the original equations, say the second one: \[ 2(2) + 4y = 16 \implies 4 + 4y = 16 \implies 4y = 12 \implies y = 3 \] Thus, the solution to the system of equations is \(x = 2\) and \(y = 3\) or \((2, 3)\). To double-check, we can substitute \(x\) and \(y\) back into both original equations to ensure they hold true. Both equations are confirmed, so the solution is valid; \( (2, 3) \) is indeed correct!